Driverless vehicles of the general type involved herein are per se known. The present invention is directed to solution of the following problem. The problem is how to orientate a vehicle in three directions including a vertical direction without elevating the vehicle body with respect to a track for the body. The problem must be solved in a manner which is simple and reliable while providing for extreme precision within a tolerance such as plus or minus 0.005 inches (0.125 mm).